Temple H. Fay's butterfly curve, lemniscate of Bernoulli, folium of Descartes, strophoid, witch of Agnesi — beautiful algebraic curves with fascinating histories.
Butterfly Curve (Temple H. Fay, 1989): r = e^(sin θ) − 2cos(4θ) + sin⁵((2θ−π)/24). Intricate polar curve resembling a butterfly's wings.